Question

One hundred fifty students are admitted in a school . They are distributed over three sections A B C . If 6 students are shifted from section A to section C , the two sections will have equal number of Students. If 4 times the students of C exceeds the number of students of section A by the number of students in section B . Find the number of students in three sections.

Answer 1

Answer:

The number of students in A ,B and C section is 42,78 and 30 respectively.

Step-by-step explanation:

Let the number of students of section A be A

Let the number of students of section A be B

Let the number of students of section C be C

Now We are given that total no. of students are 150

So, $A+B+C=150$

Now we are given that If 6 students are shifted from section A to section C , the two sections will have equal number of Students.

Students of Section A = A-6

Students of Section C = C+6

So, A.T.Q

$A-6=C+6$

$A=C+12$   --1

Now we are given that  If 4 times the students of C exceeds the number of students of section A by the number of students in section B .

$4C-A=B$  --2

Since $A+B+C=150$

So,  $B=150-(A+C)$

Substitute the value of B in 2

$4C-A=150-(A+C)$  

$4C=150-C$  

$5C=150$  

$C=30$  

Substitute In 1

$A=30+12$

$A=42$

Substitute the value of A and C in 2

$4(30)-42=B$  

$78=B$  

Hence  the number of students in A ,B and C section is 42,78 and 30 respectively.